How this calculator works
Scalar multiplication applies the same factor to every entry. Dividing by k is multiplication by 1/k, so k must be non-zero. For a square matrix, scaling every entry by k multiplies the determinant by k raised to the matrix size, because the determinant is linear in each row. The zero matrix stays the zero matrix under every scalar.
Formula
(kA)ij = k Aij. Division uses (A/k)ij = Aij / k with k not equal to zero.
Worked example
Multiplying the matrix with rows 1, 2; 3, 4 by 3 gives rows 3, 6; 9, 12. Dividing the same matrix by 2 gives rows 0.5, 1; 1.5, 2.
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Frequently asked questions
Can the scalar be zero?
You can multiply by zero, which produces the zero matrix. Division by zero is undefined, so the calculator rejects it.
How does scaling change a determinant?
An n by n matrix scaled by k has determinant k^n times the original determinant. Scaling a 3 by 3 matrix by 2 multiplies its determinant by 8.
Is scalar multiplication the same as matrix multiplication?
No. Scalar multiplication touches every entry with one number. Matrix multiplication combines rows of the first matrix with columns of the second and requires matching inner dimensions.